# 5.1: Cost-Revenue-Net Income Analysis (Need to Be in the Know) - Mathematics

The end of the month is approaching, and bills are coming due. As you sit at your kitchen table trying to figure out your budget for next month, you wonder whether you will be able to afford that concert you had been planning on attending. Some of your costs remain unchanged from month to month, such as your rent, Internet service, gym membership, and insurance. Other costs tend to fluctuate with your usage, such as your utilities, cellphone bill, vehicle fuel, and the amount of money spent on recreational activities. Together, these regular and irregular costs total to next month's costs.

Examining a few recent paycheque stubs, you calculate the average monthly net income you bring home from your hourly cashier position at Sobeys. The exact amount of each paycheque, of course, depends on how many hours you work. Besides your short-term costs, you need to start saving for next year's tuition. Therefore, your budget needs to include regular deposits into your savings account to meet that goal. Once you have put your bills, paycheques, and goals together, you hope that your budget will balance. If there is a shortfall, you will have to miss out on those concert tickets.

Budgeting at work is no different in principle from your home budget. Businesses also need to recognize the different types of costs they incur each month, some of which remain the same and some of which fluctuate. Businesses need to pay for these costs by generating revenues, which correspond to your paycheque. As with your education goals, businesses also require profits to grow. A business needs to understand all of these numbers so it can plan its activities realistically.

This section explores the various types of costs and establishes a model relating total costs to total revenues to determine total profitability levels. You will then apply this model to see how the sale of an individual product contributes to covering costs and how each product individually contributes to overall profitability.

## Types of Costs

A cost is an outlay of money required to produce, acquire, or maintain a product, which includes both physical goods and services. Costs can come in three forms:

1. A fixed cost is a cost that does not change with the level of production or sales (call this "output" for short). In other words, whether the business outputs nothing or outputs 10,000 units, these costs remain the same. Some examples include rent, insurance, property taxes, salaries unrelated to production (such as management), production equipment, office furniture, and much more. Total fixed costs are the sum of all fixed costs that a business incurs.
2. A variable cost is a cost that changes with the level of output. In other words, if the business outputs nothing there is no variable cost. However, if the business outputs just one unit (or more) then a cost appears. Some examples include material costs of products, production labour (hourly or piecework wages), sales commissions, repairs, maintenance, and more. Total variable costs are the sum of all variable costs that a business incurs at a particular level of output.
3. A blended cost is a cost that comprises both fixed cost and variable cost components. In other words, a portion of the total cost remains unchanged while another portion depends on the output. For calculation purposes, you must separate a blended cost into its fixed and variable cost components. A few examples will illustrate the concept of blended costs:
• Residential natural gas bills from Manitoba Hydro include a fixed charge per month of $14 plus charges for cubic metres of actual consumption based on transportation, distribution, and primary and supplemental gas rates. In this situation, the$14 is a fixed cost while the actual consumption of natural gas is a variable cost.
• A cell phone bill includes a fixed charge for the phone service plus any additional charges for usage, such as long distance, texting, or data.
• If employees are paid a salary plus commission, then their salaries represent fixed costs while their commissions are a variable cost.

### The Formula

In calculating business costs, fixed costs are commonly calculated on a total basis only since the business incurs these costs regardless of any production. However, variable costs are commonly calculated both on a total and per-unit basis to reveal the overall cost along with the cost associated with any particular unit of output. When these variable costs are assigned on an individual basis it is called a unit variable cost. The calculation of unit variable cost has a further benefit because it allows managers to explore how the total business costs vary at different levels of output. Formula 5.1

### How It Works

Follow these steps to calculate the unit variable cost:

• Step 1: Identify all fixed, variable, and blended costs, along with the level of output. For variable costs, understand any important elements of how the cost is structured. For blended costs, separate the costs into variable and fixed components.
• Step 2: Calculate the total variable cost ((TVC)) by totaling all variable costs at the indicated level of output. This involves taking any known unit variable costs and multiplying each by the level of output.
• Step 3: Divide the total variable cost by the total level of output by applying Formula 5.1.

Assume a company produces 10,000 units and wants to know its unit variable cost. It incurs production labor costs of $3,000, material costs of$1,875, and other variable costs totaling $1,625. Step 1: In this case, all costs are variable costs (production labour and material costs are always variable). The level of output is (n= 10,000) units. Step 2: Total all variable costs together to get (TVC) [TVC=$ 3,000+$1,875+$ 1,625=$6,500 onumber ] Step 3: Apply Formula 5.1 to arrive at (VC=$ 6,500 / 10,000=$0.65). This means that, on average, the variable cost associated with one unit of production is$0.65. ### Important Notes

The definitions of variable, fixed, and blended costs along with their typical associated examples represent a simplified view of how the real world operates. The complexities involved in real-world business costs complicate the fundamentals of managing a business. Therefore, here is how this textbook addresses the complexities of atypical operations, changing fixed costs, and decreasing unit variable costs:

1. Atypical Operations. Although there are "normal" ways that businesses operate, there are also businesses that have atypical operations. What is a fixed cost to one business may be a variable cost to another. For example, rent is usually a fixed cost. However, some rental agreements include a fixed base cost plus a commission on the operational output. These rental agreements form blended costs. This textbook does not venture into any of these atypical costs and instead focuses on common cost categorizations.
2. Changing Fixed Costs. In real-world applications, fixed costs do not remain flat at all levels of output. As output increases, fixed costs tend to move upwards in steps. For example, at a low level of output only one manager (on salary) may be needed. As output increases, eventually another manager needs to be hired, perhaps one for every 20,000 units produced. In other words, up to 20,000 units the fixed costs would be constant, but at 20,001 units the fixed costs take a step upwards as another manager is added. The model presented in this textbook does not address these upward steps and treats fixed costs as a constant at all levels of output.
3. Decreasing Unit Variable Costs. Production tends to realize efficiencies as the level of output rises, resulting in the unit variable cost dropping. This is commonly known as achieving economies of scale. As a consumer, you often see a similar concept in your retail shopping. If you purchase one can of soup, it may cost $1. However, if you purchase a bulk tray of 12 cans of soup it may cost only$9, which works out to 75¢ per can. This price is lower partly because the retailer incurs lower costs, such as fewer cashiers to sell 12 cans to one person than to sell one can each to 12 different people. Now apply this analogy to production. Producing one can of soup costs 75¢. However, a larger production run of 12 soup cans may incur a cost of only $6 instead of$9 because workers and machines can multitask. This means the unit variable cost would decrease by 25¢ per can. However, the model in this textbook assumes that unit variable costs always remain constant at any given level of output.

You are considering starting your own home-based Internet business. After a lot of research, you have gathered the following financial information:

 Dell computer $214.48 monthly lease payments Office furniture (desk and chair)$186.67 monthly rental Shaw high-speed Internet connection $166.88 per month Your wages$30 per hour Utilities $13 per month plus$0.20 per hour usage Software (and ongoing upgrades) $20.00 per month Business licenses and permits$27.00 per month Google click-through rate $10.00 per month +$0.01 per click payable as total clicks per sale

Generating and fulfilling sales of 430 units involves 80 hours of work per month. Based on industry response rates, your research also shows that to achieve your sales you require a traffic volume of 34,890 Google clicks. On a monthly basis, calculate the total fixed cost, total variable cost, and unit variable cost.

Solution

Calculate the monthly total fixed costs ((TFC)), total variable costs ((TVC)), and the unit variable cost ((VC)).

There are three different types of costs. Other known information includes:

(n= 430) units Hours = 80

How You Will Get There

Step 1:

Sort the costs into fixed and variable. Separate the components for blended costs. You can total the fixed costs to arrive at the total fixed costs, or (TFC).

Step 2:

Calculate variable costs, then total them to arrive at the total variable cost, or (TVC).

Step 3:

Apply Formula 5.1 to calculate the unit variable cost.

Perform

Step 1:

Fixed Costs

 Dell computer $214.48 Office furniture$186.67 Shaw high-speed Internet connection $166.88 Utilities (blended cost)$13.00 only Software $20.00 Business licenses / permits$27.00 Google click (blended cost) $10.00 TOTAL FIXED COSTS TFC =$638.03

Variable Costs

 Wages $30.00 per hour Utilities (blended cost)$0.20 per hour Google click (blended cost) 0.01 per click Step 2: [egin{aligned} TVC &=( 30.00 imes ext { hours })+($0.20 imes ext { hours })+($ 0.01 imes ext { Google clicks }) &=($30.00 imes 80)+($ 0.20 imes 80)+($0.01 imes 34,890)=$ 2,764.90 end{aligned} onumber ]

Step 3:

[VC=dfrac{$2,764.90}{430}=$ 6.43 onumber ]

Seven components make up the fixed costs: the computer, furniture, Internet service, fixed utilities, software, licenses/permits, and the fixed Google cost, all totaling $638.03. Three components make up the variable costs: wages, hourly utilities, and Google clicks, totaling$2,764.90. The average unit variable cost is $6.43 per unit sold. ## Net Income Using a Total Revenue and Total Cost Approach Most businesses are "for-profit" businesses, meaning that they operate to make money. In Example (PageIndex{1}), you figured out the total fixed costs, total variable costs, and the unit variable cost for your Internet business. However, you left unanswered one of the most important questions in business: If you sell the planned 430 units, are you profitable? Is there any money left after you pay for all of those fixed and variable costs? You must also remember that 430 units is just an estimate. What happens if you sell only 350 units? What happens if you sell 525 units? What happens if you decide to pay yourself a higher wage? There are no guarantees in business, and the future is always uncertain. Successful business managers plan for the future and perform many “what-if” scenarios to answer questions such as those above. This section develops a model for calculating total net income based on total revenues and total costs. The model allows managers to analyze various scenarios and determine the impact on profitability. ### The Formula Formula 5.2 ### How It Works Follow these steps to calculate net income using a total revenue and total income approach: • Step 1: Calculate the total revenue. This requires identifying the unit selling price of the product and multiplying it by the level of sales. • Step 2: Calculate your total costs. This requires identifying and separating costs into fixed and variable components. Fixed costs are totaled to arrive at the total fixed cost. Total variable costs are either known or can be calculated through multiplying the unit variable cost by the level of output. • Step 3: Calculate the net income by applying Formula 5.2. For example, assume that last month a company incurred total variable costs of$10,000 in the course of producing 1,000 units. For next month it forecasts total fixed costs of $5,000 and all variable costs remaining unchanged. Projected production for next month is 1,200 units selling for$25 each. You want to estimate next month’s net income.

Step 1: Using Formula 5.2, you calculate total revenue from (n(S)), or the total level of output multiplied by the price of the product. If you project sales of 1,200 units ((n)) at $25 each (S), then the total forecasted revenue is (1,200($ 25)=$30,000). Step 2: Total fixed costs, or (TFC), are$5,000. To get the total variable costs, you must resolve (n(VC)). You calculate the unit variable cost, or (VC), with Formula 5.1. Using the current month figures, you see (VC=$10,000 div 1,000=$ 10). If the projected level of output is 1,200 units, then the total variable costs are (1,200($10)=$ 12,000).

Step 3: Applying Formula 5.2 you have (NI= ext { Total Revenue }- ext { Total costs }=$30,000-($ 5,000+$12,000)=$ 13,000). Based on the numbers, you forecast net income of $13,000 for next month. ### Important Notes The Texas Instruments BAII Plus calculator is programmed with a version of Formula 5.2. The function is called Brkevn, and you access it by pressing 2nd and then the number six key. The relationship between the formula symbols and the calculator symbols is displayed in the table below. VariableFormula 5.2 NotationCalculator Notation Total fixed cost(TFC)FC Unit variable cost(VC)VC Price per unit(S)P (for price) Net income(NI)PFT (for profit) Level of output(n)Q (for quantity) To solve Formula 5.2 for the (PFT) or any other variable, enter data into all of the above variables except one. Keying in a variable requires inputting the value and pressing Enter. Use ­(uparrow) and (downarrow) to scroll through the display. When you are ready, scroll to the unknown variable and press (CPT). ### Paths To Success An easy way to remember Formula 5.2 is to understand what the formula represents. As explained, the calculation of (n(S)) multiplies quantity by price to produce the total revenue. The ((TFC + n(VC)) takes the total fixed costs and adds the total variable costs (which is a function of quantity multiplied by unit variable cost) to arrive at the total cost. Therefore, Formula 5.2 expressed more simply is: [ ext { Net Income }= ext { Total Revenue }- ext { Total Cost } onumber] Exercise (PageIndex{1}): Give It Some Thought In the following situations, explain what would happen to net income and why. 1. The selling price is raised. 2. The hourly wages of production workers are increased to match the increase in the consumer price index. 3. The level of output decreases. 4. Your insurance company lowers your insurance premiums because your company has had no claims in the past year. Answer 1. Net income increases because the total revenues increase with no similar increase in costs. 2. Net income decreases because the hourly wages of production workers are variable costs. If the costs go up, then less money is left over. 3. Net income decreases because both total revenue and total variable costs drop; however, the fixed costs remain the same, so there is less revenue to cover proportionally higher costs. 4. Net income increases because the insurance premium is a fixed cost that has become smaller. With lower costs, more money is left over. Recall from Example (PageIndex{1}) that you are considering starting your own home-based Internet business. The following information is known: (FC) =$638.03, (VC) = $6.43, forecasted (n) = 430 Based on these numbers, calculate: 1. The forecasted net income if your price per unit is$10.
2. The dollar change in net income if you decide to pay yourself a higher wage of $35.38 per hour instead of$30.00 per hour while still working 80 hours. Note the total variable costs excluding wages were $364.90. 3. The dollar change in net income if sales are 30% lower than your initial forecast, ignoring part (b) calculations. Solution 1. You need to determine net income ((NI)) using the revenue and cost numbers. 2. Recalculate the total variable cost ((TVC)) to determine the impact of the higher wage. Then calculate the change in net income ((NI)). 3. Modify the level of output ((n)) and calculate the change in net income ((NI)). What You Already Know The costs, level of output, and price are known: (FC) =$638.03, (VC) = $6.43, forecasted (n) = 430, (S) =$10

For part (b), the total variable costs excluding wages are known:

(TVC) (excluding wages) = $364.90 New wage =$35.38

Hours = 80

For part (c), the change in the level of output is known:

(Delta \%=-30 \%)

How You Will Get There

a.

Step 1:

Calculate total revenue at the forecasted output.

Step 2:

Calculate total costs at the forecasted output.

Step 3:

Apply Formula 5.2.

b.

Step 1:

Total revenue is unchanged since the output has not changed.

Step 2:

Fixed costs are unchanged. Recalculate the total variable costs by adding the new wages to the total variable costs excluding wages. By rearranging Formula 5.1, you can see (TVC=n(VC)). Therefore, substitute (TVC) in place of (n(VC)) in Formula 5.2.

Step 3:

Apply Formula 5.2 to recalculate the new net income. Compare to net income in part (a) and determine the change.

c.

Step 1:

The revised level of output is a percent change calculation where (Delta \%=-30 \%) and (OLD = 430). Solve Formula 3.1 for New. Once New is known, recalculate total revenue.

Step 2:

Fixed costs are unchanged. Recalculate total variables costs using the revised level of output.

Step 3:

Apply Formula 5.2 to recalculate the new net income. Compare to net income in part (a) and determine the change.

Perform

a.

Step 1:

( ext { Total revenue }=n(S)=430($10)=$ 4,300)

Step 2:

(TFC=$638.03); (TVC=n(VC)=430($ 6.43)=$2,764.90) Step 3: (NI=s 4,300-($ 638.03+$2,764.90)=$ 897.07)

b.

Step 1:

( ext { Total revenue }=$4,300) Step 2: (TFC=$ 638.03); (TVC=$364.90+($ 35.38 imes 80 ext { hours })=3,195.30) Step 3: (egin{aligned} NI&= 4,300-($638.03+$ 3,195.30)=$466.67 ext { Change in } NI&=$ 466.67-$897.07=-$ 430.40 end{aligned})

c.

Step 1:

(egin{aligned} -30 \%&=dfrac{ ext{New}-430}{430} imes 100 -129&= ext { New }-430 301&= ext { New }end{aligned})

( ext { Total revenue } =301($10)=$ 3,010)

Step 2:

(TFC=$638.03 ; TVC=301($ 6.43)=1,935.43) Step 3: (egin{aligned} NI&= 3,010-($638.03+$ 1,935.43)=$436.54 ext { Change in } NI&=$ 436.54-$897.07=-$ 460.53 end{aligned})

Calculator Instructions

FCVCPPFTQ

*First use (Delta \%) function to calculate this number:

OLDNEW%CH#PD

Under the initial scenario, a net income of $897.07 on sales of 430 units is forecast. If you pay yourself a higher wage of$35.38 per hour, your net income decreases by $430.40 to$466.67. If your forecast is inaccurate and is lower by 30%, then your net income is reduced by $460.53, resulting in a lower net income of$436.54.

## Net Income Using a Total Contribution Margin Approach

In Example (PageIndex{2}), you learned that if you sell the projected 430 units of product for your Internet business, the total net income is $897.07. What if you sold 431 units of the product? How would your net income change? Clearly it should rise, but by how much? One approach to answering this question is to rerun the numbers through Formula 5.2, revising the total revenues and total variable costs to calculate a new net income. This new net income can then be compared against the existing net income to determine how it changed. This is a multi-step approach and involves a lot of work. An alternative approach explored in this section involves using a unit contribution margin to calculate the net income. The benefit of this approach is that with minimal calculations you can easily assess the impact of any change in the level of output. In accounting and marketing, the contribution margin is the amount that each unit sold adds to the net income of the business. This approach allows you to understand the impact on net income of each unit sold, and Section 5.2 will explain its further benefit of allowing for a straightforward calculation of a break-even point. The contribution margin determines on a per-unit basis how much money is left over after unit variable costs are removed from the price of the product. This leftover money is then available to pay for the fixed costs. Ultimately, when all fixed costs have been paid for, the leftover money becomes the profits of the business. If not enough money is left over to pay for the fixed costs, then the business has a negative net income and loses money. ### The Formula The difference between the increase in the total revenue and the increase in the total variable costs is how much the sale of an individual product contributes toward the change in your net income. Formula 5.3 expresses this relationship. Formula 5.3 If you have no units sold, your net income is negative and equal to the total fixed costs associated with your business, since there is no offsetting revenue to pay for those costs. With each unit sold, the contribution margin of each product is available to pay off the fixed costs. Formula 5.4 expresses this relationship when calculating net income. Formula 5.4 ### How It Works Follow these steps to calculate the net income using a contribution margin approach: Step 1: If unit information is known, apply Formula 5.3 and calculate the unit contribution margin by subtracting the unit variable cost from the selling price. This may or may not require you to use Formula 5.1 to calculate the unit variable cost. Step 2: Calculate the total contribution margin by multiplying the contribution margin with the associated level of output. Step 3: Calculate the total fixed costs by adding all fixed costs. Step 4: Based on the level of output, calculate the net income by applying Formula 5.4. For example, using the contribution margin approach, calculate the net income for a product that sells for$75, has unit variable costs of $31, total fixed costs of$23,000, and total sales of 800 units.

Step 1: The unit contribution margin is calculated from Formula 5.3. If the product sells for $75 and has unit variable costs of$31, then (CM=$75-$ 31=$44). This means that every unit sold has$44 left over to contribute toward fixed costs.

Step 2: Now convert that into a total contribution margin. The first part of Formula 5.4 calculates total contribution margin through (n(CM)). With sales of 800 units, the total contribution margin is (800($44)=$ 35,200).

Step 3: Total fixed costs are known: (TFC=$23,000). Step 4: Apply Formula 5.4, which translates to ( ext { Net Income }= ext { Total contribution margin - Total fixed costs }), or ($ 35,200-$23,000=$ 12,200).

### Paths To Success

When you work with Formula 5.4, sometimes unit information may not be known. Instead, you might just have a single aggregate number representing the total contribution margin for which somebody has already taken the total revenue and subtracted the total variable costs. In this case, skip step 1 and take the provided total contribution margin as the answer for step 2 with no calculations necessary.

Continuing with Examples (PageIndex{1}) and (PageIndex{2}), calculate the unit contribution margin and net income using the contribution margin approach. From the previous examples, recall the unit variable cost is $6.43, unit selling price is$10, total fixed costs are $638.03, and the projected sales are 430 units. Solution Calculate the unit contribution margin ((CM)) followed by the net income ((NI)) using the contribution margin approach. What You Already Know The cost, price, and sales information are known: (VC=$ 6.43, S=$10) (TFC=$ 638.03, n=430)

How You Will Get There

Step 1:

Calculate the unit contribution margin using Formula 5.3.

Step 2:

Calculate the total contribution margin by multiplying the unit contribution margin times the level of output.

Step 3:

Determine the total fixed costs.

Step 4:

To calculate net income, apply Formula 5.4.

Perform

Step 1:

[CM=$10.00-$ 6.43=$3.57 onumber ] Step 2: [n(CM)=430($ 3.57)=$1,535.10 onumber ] Step 3: [TFC=$ 638.03 onumber ]

Step 4:

[NI=$1,535.10-$ 638.03=$897.07 onumber ] Calculator Instructions FCVCPPFTQ 638.036.4310Answer: 897.07430 When a product sells for$10, $6.43 goes toward paying for the variable costs of your business, leaving$3.57 as your unit contribution margin. This means that for every unit increase in sales, your net income rises by $3.57. Thus, if you sell 430 units you have a total contribution margin of$1,535.10, which results in a net income of $897.07 after removing fixed costs of$638.03.

## Contribution Rates

It is difficult to compare different products and their respective dollar amount contribution margins if their selling prices and costs vary widely. For example, how do you compare a unit contribution margin of $1,390 (selling price of$2,599.99) on a big screen television to a unit contribution margin of $0.33 on a chocolate bar (selling price of$0.67)? On a per-unit basis, which contributes relatively more to fixed costs? To facilitate these comparisons, the products must be placed on equal terms, requiring you to convert all dollar amount contribution margins into percentages. A contribution rate is a contribution margin expressed as a percentage of the selling price.

### The Formula

Your choice between two formulas for calculating a contribution rate depends on whether you have unit information or only aggregate information. Both formulas are adaptations of Formula 2.2 (Rate, Portion, Base).

If unit information is known, including the unit variable cost and unit selling price, then calculate the contribution rate using unit information as expressed in Formula 5.5. Formula 5.5

If any unit information, including the unit variable cost or unit selling price, is unknown or unavailable, then you cannot apply Formula 5.5. Sometimes only aggregate information is known. When total revenue and total variable costs for any product are known or can at least be calculated, then you must calculate the contribution rate from the aggregate information as expressed in Formula 5.6. Formula 5.6

### How It Works

Follow these steps to calculate a contribution rate:

Step 1: Identify the required variables and calculate the margin, if needed.

• If unit information is known, this requires you to calculate the unit contribution margin. Otherwise, calculate the unit contribution margin by applying Formula 5.3. You must identify the unit selling price.
• If aggregate information is known, you need to identify total revenue and total variable costs.

Step 2: Calculate the contribution rate.

• If unit information is known, apply Formula 5.5.
• If only aggregate information is known, apply Formula 5.6.

As an example of these steps, recall earlier that you wanted to compare the relative contributions of the big screen television and the chocolate bar. The television sells for $2,599.99 and has a unit contribution margin of$1,390. The chocolate bar sells for $0.67 and has a unit contribution margin of$0.33. Notice that the information being provided is on a per-unit basis. Calculate the contribution rate of each product.

Step 1: The contribution margins are known. For the television, (CM) = $1,390, and for the chocolate bar, (CM) =$0.33.

Step 2: Applying Formula 5.5, the television (CR=$1,390.00 div$ 2,599.99 imes 100=53.4617 \%), while the chocolate bar (CR=$0.33 div$ 0.67 imes 100=49.2537 \%). It is now evident from the contribution rate that 4.208% more of the television’s selling price is available to pay for fixed costs as compared to the chocolate bar’s price.

Now change the facts. This time, assume there is no unit information. Instead, the television’s total revenue is $129,999.50 and associated total variable costs are$60,499.50. The chocolate bar has total revenue of $3,886.00 with total variable costs of$1,972.00. Based on this information, you are to determine the product with the higher contribution rate.

Step 1: The aggregate numbers are known for both products. For the television, (TR = $129,999.50) and (TVC =$60,499.50). For the chocolate bar, (TR = $3,886.00) and (TVC =$1,972.00).

Step 2: Applying Formula 5.6, the television (CR=dfrac{$129,999.50-$ 60,499.50}{$129,999.50} imes 100=53.4617 \%) while the chocolate bar (CR=dfrac{$ 3,886-$1,972}{$ 3,886} imes 100=49.2537 \%) You have reached the same conclusion as above. Exercise (PageIndex{2}): Give It Some Thought

In each of the following situations, what would happen to the contribution rate and why?

1. The selling price is raised.
2. The hourly wages of production workers are increased to match the increase in the consumer price index.
3. The level of output decreases.
1. The contribution rate increases, since raising the price increases the unit contribution margin.
2. The contribution rate decreases, since total variable costs rise, eroding some of the unit contribution margin.
3. There is no effect on the contribution rate. The level of output is not a factor in calculating the contribution rate.
4. There is no effect on the contribution rate since the insurance premiums are a fixed cost. Fixed costs are not a factor in calculating contribution rates

Continuing with your ongoing Internet business from the three previous examples, calculate the contribution rate using both the unit and aggregate methods and show how they arrive at the same number. Remember that you are selling products for $10 each, your unit contribution margin is$3.57, total revenue is projected at $4,300, and total variable costs are$2,764.90.

Solution

Your goal is to calculate the contribution rate ((CR)) using both the unit and aggregate methods.

Step 1:

Prices, margins, revenue, and costs are known:

(S=$10, CM=$ 3.57)

(TR=$4,300, TVC=$ 2,764.90)

How You Will Get There

Step 2a:

Using the unit method, apply Formula 5.5.

Step 2b:

Using the aggregate method, apply Formula 5.6.

Perform

Step 2a:

(CR=dfrac{$3.57}{$ 10.00} imes 100=35.7 \%)

Step 2b:

(CR=dfrac{54,300.00-$2,764.90}{$ 4,300.00} imes 100=35.7 \%)

Under both the unit and aggregate method, your contribution rate equals 35.7%. This means that every time you sell a $10 product, 35.7% of the revenue remains after recovering the cost of the product. ## Putting It All Together You have studied costs, volume, and net income in this section. So far, you have considered each of these concepts separately while you worked through the various applications. It is time to put the types of costs, unit variable cost, net income, sales, contribution margin, and contribution rate together so that you can see all of these concepts in a single scenario. Look at the following example. Example (PageIndex{5}): Running a Pizza Delivery Business In the commercial section of the newspaper you come across an ad for a pizza delivery business for sale. Upon inquiry, you discover that the owner, who wants to sell the business and then retire, has four salaried employees and owns two delivery vehicles. He invites you to look through his books, where you acquire the following information:  Employees:Owner's salaryEmployee salaries and premiums$5,000 per month$2,000 per month each Business:PhoneBusiness insuranceBuilding lease$85 per month$3,600 per year$2,000 per month Delivery Vehicles:Car insuranceFuelOil changesVehicle maintenance and repairs $1,200 per year per vehicle$1,125 per month per vehicle$225 per month per vehicle$562.50 per month per vehicle Operations: Pizza ingredients, materials, and packagingSelling price of pizzaAverage number of pizzas sold $19,125 per month$9 per pizza4,500 per month

Assume that this is all of the key information. You need to understand this business and therefore want to determine:

1. A unit variable cost
2. A typical monthly net income for the business
3. The contribution margin per pizza
4. The contribution rate

Solution

All calculations require the sorting of costs into fixed and variable components, which will be your first step. You then calculate a unit variable cost ((VC)) using the historical operations information. Once you obtain this, you can calculate the net income ((NI)), contribution margin ((CM)), and contribution rate ((CR)).

You have unit information on costs, volume, and revenue, as listed above.

How You Will Get There

a. Unit variable cost:

Step 1:

Sort the costs into fixed and variable categories. Total the monthly fixed costs.

Step 2:

Total the monthly variable costs.

Step 3:

Calculate the unit variable cost by applying Formula 5.1.

b. Net income:

Step 1:

Calculate total revenue at the level of output.

Step 2:

Calculate total costs at the level of output.

Step 3:

Calculate monthly net income by applying Formula 5.2.

c. and d. Contribution margin and rate:

Step 1:

Calculate the contribution margin by applying Formula 5.3.

Step 2:

Calculate the contribution rate by applying Formula 5.5.

Perform

a. Unit variable cost:

Steps 1 and 2:

Fixed Costs per Month

 Owner’s salary $5,000 Employee salaries and premiums$2,000 × 4 = $8,000 Car insurance$1,200 × 2 cars ÷ 12 months = $200 Phone$85 Business insurance $3,600 ÷ 12 months =$300 Building lease $2,000 TOTAL FIXED COSTS TFC =$15,585 per month

Variable Costs per Month

 Fuel $1,125 × 2 vehicles =$2,250 Oil changes $225 × 2 vehicles =$450 Vehicle maintenance and repairs $562.50 × 2 vehicles =$1,125 Pizza ingredients, materials, and packaging $19,125 TOTAL VARIABLE COSTS TVC =$22,950 per month

Step 3:

(VC=dfrac{$2,250+$ 450+$1,125+$ 19,125}{4,500 ext { pizzas }}=$5.10) per pizza b. Net income: Step 1: [ ext { Total Revenue }=4,500($ 9)=$40,500 onumber ] Step 2: [TFC=$ 15,585 ; TVC=4,500($5.10)=$ 22,950 onumber ]

Step 3:

[NI=$40,500-($ 15,585+$22,950)=$ 40,500-$38,535=$ 1,965 onumber ]

c. Contribution margin and rate:

Step 1:

[CM=$9.00-$ 5.10=$3.90 onumber ] Step 2: [CR=dfrac{53.90}{59.00} imes 100=43. overline{3} \% onumber ] Calculator Instructions FCVCPPFTQ 155855.19Answer: 1,9654500 This is a profitable business. For an average month, the business incurs$15,585 in fixed costs along with $22,950 in variable costs, which works out to a unit variable cost of$5.10 for each of the 4,500 pizzas sold. With total revenue of $40,500, after removing both fixed and variable costs, net income is$1,965 per month. Every pizza, after paying for the unit variable costs, has $3.90, or (43. overline{3} \%), left over. ## Leibniz To maximize its profit, Beautiful Cars chooses a point on its demand curve where its isoprofit curve is tangent to the demand curve. We have seen this diagrammatically, and in this Leibniz we prove that the tangency point is optimal by solving the profit-maximization problem mathematically. The demand curve for Beautiful Cars slopes downward. When choosing a price, the managers of the firm know that the more cars they produce, the lower the price they will need to set in order to sell them. In the text, we drew the demand curve as a downward-sloping straight line, but in reality it is unlikely to be straight. Here we express it more generally as a function. The maximum price at which cars can be sold is given by: where is a strictly decreasing function (). When we write the demand relationship like this, with price as a function of quantity, we call the inverse demand function. When it is written the other way around, with quantity in terms of price, the function is called the demand function. Beautiful Cars’ profit, , is equal to its total revenue minus its total cost: The company wishes to set price and quantity so as to maximize its profit, subject to the constraint that the price is one that buyers are willing to pay. Its problem is therefore to: The simplest way to solve this optimization problem is by the method of substitution. We use the constraint to substitute for , giving profit as a function of alone: To find the value of that maximizes this function, we differentiate with respect to (using the product differentiation rule, ): The first-order condition for optimization is , which may be rearranged as follows: The profit-maximizing quantity, , satisfies this equation. If we knew the specific form of the functions and , we could try to solve the equation to find explicitly. The profit-maximizing price could then be calculated as . But without knowing the functions, we can still interpret the first-order condition. We know that the optimal value of is on the demand curve, so , and that is marginal cost (MC). So the first-order condition can be written: The left-hand side of this equation is the slope of the demand curve. We showed in Leibniz 7.4.1 that the right-hand side is the slope of the isoprofit curve. Thus the first-order condition tells us precisely that the profit-maximizing choice lies at a point of tangency between the demand and isoprofit curves. For Beautiful Cars, this is point E in Figure 7.11, reproduced below as Figure 1. Figure 1 The profit-maximizing choice of price and quantity for Beautiful Cars. Notice that the left-hand side of the first-order condition, , is negative, so the right-hand side must also be negative. The profit-maximizing point lies on the downward-sloping part of an isoprofit curve, where price exceeds marginal cost. Read more: Sections 6.4, 7.4, and 8.1 of Malcolm Pemberton and Nicholas Rau. 2015. Mathematics for economists: An introductory textbook, 4th ed. Manchester: Manchester University Press. ## Calculating A Company's Net Income And Why It Matters Source: Flickr user taxcredits.net If the old investing adage "stocks follow earnings over time" is correct, then a company's net income rates must-know status. Fortunately, net income isn't a complex calculation and net income data is commonly reported by financial websites and within corporate financial documents. Since understanding how net income is calculated and what net income tells you as an investor can be valuable, let's consider it more closely. What is net income? Net income is a company's total bottom line profit and as such, net income offers insight into the attractiveness of a business. Net income is computed using the following calculation: Total Revenue-(costs of goods sold + operating expenses + other gains or losses + other expenses + depreciation + interest expense + taxes) Net income is found at the bottom of a company's income statement and income statements are available via a company's quarterly financial reports, which can be found on a company's investor relations website or by accessing a company's quarterly 10-Q report or annual 10-K report that are filed with the Securities and Exchange Commission. What net income is telling investors Net income tells investors whether or not a company makes money and as such, it offers insight into whether or not a company's business may succeed or fail. Net income also provides investors with a benchmark that can be used to compare a company's performance to its past or future performance, or to compare one company's performance to the performance of a competitor. Company A is a beverage company and its annual income statement is presented below. In this income statement, you can see that Company A reports$46 billion in sales and that the cost of producing that revenue totaled $17.9 billion, resulting in a gross profit of$28.1 billion.

That's interesting, but net income can be more useful because subtracting expenses associated with day-to-day operations, such as selling, general, and administrative costs (SG&A), interest paid on debt, and income taxes paid, shows how much money is leftover for investors after all of the various puts and takes are considered.

In the case of Company A, adjusting gross profit by other income and various expenses, such as the $18.4 billion that the company spent on SG&A, and the$2.2 billion it spent on taxes, leaves us with a net income of $7.1 billion. Without digging deeper, an investor is left knowing only that Company A is profitable in its most recent year. However, if an investor considers Company A's net income relative to its net income in prior years, a clearer understanding of profitability is achieved. In this case, an investor discovers that Company A's net income is lower than it was in each of the preceding two years. Because Company A's net income has slipped, an investor now knows that more research is necessary to explain the profit slump. Similarly, comparing Company A's net income to its competitors can also offer additional insight into how attractive the company may be as an investment. In the following table, Company B -- a main rival of Company A -- reports that its revenue is$66.7 billion, its gross profit is $35.8 billion, and its net income is$6.5 billion during the same period as Company A. Company A's net income is higher than Company B's, but what what may make Company A more interesting to an investor than Company B is that more of Company A's revenue is falling to the bottom line than Company B's. Dividing each company's net income by their revenue shows that Company A's net income is 15.4% of sales, while Company B's is 9.7% of sales.

Tying-it-together

Net income is an important financial metric, but net income can be manipulated by one-time charges and investment gains. For that reason, net income is only one of many things that investors should consider when evaluating a company for an investment. Regardless, net income can offer valuable insight that can be used to see if a company's profitability is improving or deteriorating and to discover is a company is more or less profitable then its peers.

## Null Hypothesis Significance Testing

### 11.5.2 Exploring model predictions (posterior predictive check)

A Bayesian analysis only indicates the relative credibilities of the various parameter values or models under consideration. The posterior distribution only tells us which parameter values are relatively less bad than the others. The posterior does not tell us whether the least bad parameter values are actually any good.

For example, suppose we believe that a coin is a heavily biased trick coin, and either comes up heads 99% of the time, or else comes up tails 99% of the time we just don't know which direction of bias it has. Now we flip the coin 40 times and it comes up heads 30 of those flips. It turns out that the 99%-head model has a far bigger posterior probability than the 99%-tail model. But it is also the case that the 99%-head model is a terrible model of a coin that comes up heads 30 out of 40 flips!

One way to evaluate whether the least unbelievable parameter values are any good is via a posterior predictive check . A posterior predictive check is an inspection of patterns in simulated data that are generated by typical posterior parameters values. The idea of a posterior predictive check is as follows: If the posterior parameter values really are good descriptions of the data, then the predicted data from the model should actually “look like” real data. If the patterns in the predicted data do not mirror the patterns in the actual data, then we are motivated to invent models that can produce the patterns of interest.

This use of the posterior predictive check is suspiciously like NHST: We start with a hypothesis (i.e., the least unbelievable parameter values), and we generate simulated data as if we were repeating our intended experiment over and over. Then we see if the actual data are typical or atypical in the space of simulated data. If we were to go further, and determine critical values for false alarm rates and then reject the model if the actual data fall in its extreme tails, then we would indeed be doing something tantamount to NHST. Some authors do promote this sort of “Bayesian p value.” But I prefer to keep posterior predictive checks fully Bayesian. The goal of the posterior predictive check is to drive intuitions about the qualitative manner in which the model succeeds or fails, and about what sort of novel model formulation might better capture the trends in the data. Once we invent another model, then we can use Bayesian methods to quantitatively compare it with the other models. For further discussion, see Section 17.5.1 andKruschke (2013b).

## Comparing P/E ratios

Here are the best comparisons to use for the P/E ratio:

### Peers

For the most part, competitors in an industry have similar businesses and earnings models. That means P/E ratios in the industry should be around the same, and differences to the positive likely reflect business quality or growth potential. If you think a company has a superior business but it still has a low P/E ratio, then it may be a good investment.

### History

Looking at a stock's P/E ratio history is one of the best ways to avoid buying stocks with perpetually low P/E ratios. If a value stock's P/E ratio is unfavorable and has been for years, then what's the specific catalyst that will make it trade at higher prices in the future? If a growth stock is trading at its highest-ever P/E ratio, but the growth rate is starting to decline, then the stock's price may soon fall.

If a company is close to the beginning of its life cycle and is still proving out its business model, you can expect multiple expansions by the company over the coming years and may be willing to accept a high P/E ratio. If a company is a slow- or no-growth stalwart, be wary of multiple contractions and accept only low P/E ratios.

### Growth

Since a company that is growing rapidly may be worth a high P/E ratio, you can compare among ratios by also calculating a company's P/E ratio as a multiple of the company's projected earnings growth rate. Simply divide a company's P/E ratio by either the earnings growth rate from the past few years or an analyst-supplied projection for the next few years. Companies with low — say, below 1 — P/E-to-earnings-growth (PEG) ratios may be worth somewhat higher P/E ratios.

## The relationship among deficiency needs and growth needs: An empirical investigation of Maslow's theory

Maslow's (1954) influential theory suggests that children's ability to be motivated by “growth needs” (e.g., academic achievement) first requires satisfaction of “deficiency needs” (e.g., safety needs, love/belonging needs). Given the vast number of children experiencing deficiency needs, a better understanding of these relationships can serve as a prerequisite for establishing conditions that maximize learning outcomes. In this study, we examined Maslow's model by testing the relationship between deficiency needs variables and growth needs variables. Our sample was comprised of 390 economically disadvantaged students attending more than 40 schools in a Midwestern state in the U.S. Deficiency needs were measured using factors derived from a parent survey and growth needs were measured using factors derived from a parent survey and results from an individually-administered norm-referenced achievement test. Regression analyses were conducted to determine the relationship between a set of two deficiency needs variables (i.e., safety needs and love/belonging needs) and four academic achievement outcome variables. All four regression models were significant, revealing a positive relationship between deficiency needs and growth needs. The factor most significantly related to achievement outcomes was access to health and dental care (a safety need). Implications for research and practice are discussed.

### Highlights

► We tested the relationship between deficiency and growth needs posited by Maslow. ► Data were collected as part of a case management program in 40 Midwest schools. ► We found a positive relationship between deficiency needs and growth needs. ► Access to health/dental care was strongly related to achievement. ► Implications for service programs are discussed.

## Poverty Guidelines

The 2021 poverty guidelines are in effect as of January 13, 2021
Federal Register Notice, February 1, 2021 - Full text.

2021 POVERTY GUIDELINES FOR THE 48 CONTIGUOUS STATES AND THE DISTRICT OF COLUMBIA
Persons in family/household Poverty guideline
For families/households with more than 8 persons, add $4,540 for each additional person. 1$12,880
2 $17,420 3$21,960
4 $26,500 5$31,040
6 $35,580 7$40,120
8 $44,660 2021 POVERTY GUIDELINES FOR ALASKA Persons in family/household Poverty guideline For families/households with more than 8 persons, add$5,680 for each additional person.
1 $16,090 2$21,770
3 $27,450 4$33,130
5 $38,810 6$44,490
7 $50,170 8$55,850
2021 POVERTY GUIDELINES FOR HAWAII
Persons in family/household Poverty guideline
For families/households with more than 8 persons, add $5,220 for each additional person. 1$14,820
2 $20,040 3$25,260
4 $30,480 5$35,700
6 $40,920 7$46,140
8 $51,360 ### Resources The separate poverty guidelines for Alaska and Hawaii reflect Office of Economic Opportunity administrative practice beginning in the 1966-1970 period. Note that the poverty thresholds &mdash the original version of the poverty measure &mdash have never had separate figures for Alaska and Hawaii. The poverty guidelines are not defined for Puerto Rico, the U.S. Virgin Islands, American Samoa, Guam, the Republic of the Marshall Islands, the Federated States of Micronesia, the Commonwealth of the Northern Mariana Islands, and Palau. In cases in which a Federal program using the poverty guidelines serves any of those jurisdictions, the Federal office which administers the program is responsible for deciding whether to use the contiguous-states-and-D.C. guidelines for those jurisdictions or to follow some other procedure. The poverty guidelines apply to both aged and non-aged units. The guidelines have never had an aged/non-aged distinction only the Census Bureau (statistical) poverty thresholds have separate figures for aged and non-aged one-person and two-person units. Programs using the guidelines (or percentage multiples of the guidelines &mdash for instance, 125 percent or 185 percent of the guidelines) in determining eligibility include Head Start, the Supplemental Nutition Assistance Program (SNAP), the National School Lunch Program, the Low-Income Home Energy Assistance Program, and the Children&rsquos Health Insurance Program. Note that in general, cash public assistance programs (Temporary Assistance for Needy Families and Supplemental Security Income) do NOT use the poverty guidelines in determining eligibility. The Earned Income Tax Credit program also does NOT use the poverty guidelines to determine eligibility. For a more detailed list of programs that do and don&rsquot use the guidelines, see the Frequently Asked Questions (FAQs). The poverty guidelines (unlike the poverty thresholds) are designated by the year in which they are issued. For instance, the guidelines issued in January 2021 are designated the 2021 poverty guidelines. However, the 2021 HHS poverty guidelines only reflect price changes through calendar year 2020 accordingly, they are approximately equal to the Census Bureau poverty thresholds for calendar year 2020. (The 2020 thresholds are expected to be issued in final form in September 2021 a preliminary version of the 2020 thresholds is now available from the Census Bureau.) The poverty guidelines may be formally referenced as &ldquothe poverty guidelines updated periodically in the Federal Register by the U.S. Department of Health and Human Services under the authority of 42 U.S.C. 9902(2).&rdquo There are two slightly different versions of the federal poverty measure: poverty thresholds and poverty guidelines. The poverty thresholds are the original version of the federal poverty measure. They are updated each year by the Census Bureau. The thresholds are used mainly for statistical purposes &mdash for instance, preparing estimates of the number of Americans in poverty each year. (In other words, all official poverty population figures are calculated using the poverty thresholds, not the guidelines). Poverty thresholds since 1973 (and for selected earlier years) and weighted average poverty thresholds since 1959 are available on the Census Bureau&rsquos Web site. For an example of how the Census Bureau applies the thresholds to a family&rsquos income to determine its poverty status, see &ldquoHow the Census Bureau Measures Poverty&rdquo on the Census Bureau&rsquos web site. The poverty guidelines are the other version of the federal poverty measure. They are issued each year in the Federal Register by the Department of Health and Human Services (HHS). The guidelines are a simplification of the poverty thresholds for use for administrative purposes &mdash for instance, determining financial eligibility for certain federal programs. The poverty guidelines are sometimes loosely referred to as the &ldquofederal poverty level&rdquo (FPL), but that phrase is ambiguous and should be avoided, especially in situations (e.g., legislative or administrative) where precision is important. Key differences between poverty thresholds and poverty guidelines are outlined in a table under Frequently Asked Questions (FAQs). See also the discussion of this topic on the Institute for Research on Poverty&rsquos web site. The January 2021 poverty guidelines are calculated by taking the 2019 Census Bureau’s poverty thresholds and adjusting them for price changes between 2019 and 2020 using the Consumer Price Index (CPI-U). The poverty thresholds used by the Census Bureau for statistical purposes are complex and are not composed of standardized increments between family sizes. Since many program officials prefer to use guidelines with uniform increments across family sizes, the poverty guidelines include rounding and standardizing adjustments. ## New To This Edition Solution Walkthrough Videos for Managerial Accounting: Author Paul Kimmel has expanded the number of Solution Walkthrough Videos, now with more walkthroughs focusing on the managerial accounting part of the course. Interactive Tutorials: The popular Interactive Tutorials are responsively designed to fit nearly on all screens, giving students the opportunity to study anytime, anywhere, and they are ADA compliant. Revised Test Bank: With 30% new or revised content, the test bank makes it easier for instructors to tailor examinations according to multiple learning outcomes. Excel Function Videos Related to Data Analytics: Data Analytics is a hot topic in accounting, and these videos help students learn the competencies they need to be successful in their careers. ## 19 Personal Financial Ratios You Need to Know Your personal financial statements provide you with an indication of your financial condition and the personal financial ratios help you to know your net worth and to give you the financial position insights that your personal financial statement alone cannot reveal. I’ve been using my personal finance ratios to invest for financial freedom. I launched a book that highlights how to invest for financial freedom called Dividend Investing Your Way to Financial Freedom. Download a sample of how I plan to achieve financial freedom from investing: ## How to Analyze Your Business Using Financial Ratios Many small and mid-sized companies are run by entrepreneurs who are highly skilled in some key aspect of their business&mdashperhaps technology, marketing or sales&mdashbut are less savvy in financial matters. The goal of this document is to help you become familiar with some of the most powerful and widely-used tools for analyzing the financial health of your company. Some of the names&mdash"common size ratios" and "liquidity ratios," for example&mdashmay be unfamiliar. But nothing in the following pages is actually very difficult to calculate or very complicated to use. And the payoff to you can be enormous. The goal of this document is to provide you with some handy ways to look at how your company is doing compared to earlier periods of time, and how its performance compares to other companies in your industry. Once you get comfortable with these tools you will be able to turn the raw numbers in your company's financial statements into information that will help you to better manage your business. WHAT YOU SHOULD KNOW BEFORE GETTING STARTED [top] For most of us, accounting is not the easiest thing in the world to understand, and often the terminology used by accountants is part of the problem. "Financial ratio analysis" sounds pretty complicated. In fact, it is not. Think of it as "batting averages for business." If you want to compare the ability of two Major League home-run sluggers, you are likely to look at their batting averages. If one is hitting .357 and the other's average is .244, you immediately know which is doing better, even if you don't know precisely how a batting average is calculated. In fact, this classic sports statistic is a ratio: it's the number of hits made by the batter, divided by the number of times the player was at bat. (For baseball purists, those are "official at-bats," which is total appearances at the plate minus walks, sacrifice plays and any times the player was hit by a pitch.) You can think of the batting average as a measure of a baseball player's productivity it is the ratio of hits made to the total opportunities to make a hit. Financial ratios measure your company's productivity. There are many ratios you can use, but they all measure how good a job your company is doing in using its assets, generating profits from each dollar of sales, turning over inventory, or whatever aspect of your company's operation that you are evaluating. Financial Ratio Analysis The use of financial ratios is a time-tested method of analyzing a business. Wall Street investment firms, bank loan officers and knowledgeable business owners all use financial ratio analysis to learn more about a company's current financial health as well as its potential. Although it may be somewhat unfamiliar to you, financial ratio analysis is neither sophisticated nor complicated. It is nothing more than simple comparisons between specific pieces of information pulled from your company's balance sheet and income statement. A ratio, you will remember from grammar school, is the relationship between two numbers. As your math teacher might have put it, it is "the relative size of two quantities, expressed as the quotient of one divided by the other." If you are thinking about buying shares of a publicly-traded company, you might look at its price-earnings ratio. If the stock is selling for$60 per share, and the company's earnings are $2 per share, the ratio of price ($60) to earnings ($2) is 30 to 1. In common usage, we would say the "P/E ratio is 30." Financial ratio analysis can be used in two different but equally useful ways. You can use them to examine the current performance of your company in comparison to past periods of time, from the prior quarter to years ago. Frequently this can help you identify problems that need fixing. Even better, it can direct your attention to potential problems that can be avoided. In addition, you can use these ratios to compare the performance of your company against that of your competitors or other members of your industry. Remember that the ratios you will be calculating are intended simply to show broad trends and thus to help you with your decision-making. They need only be accurate enough to be useful to you. Don't get bogged down calculating ratios to more than one or two decimal places. Any change that is measured in hundredths of a percent will almost certainly have no meaning. Make sure your math is correct, but don't agonize over it. A ratio can be expressed in several ways. A ratio of two-to-one can be shown as: In these pages, when we present a ratio in the text it will be written out, using the word "to." If the ratio is in a formula, the slash sign (/) will be used to indicate division. As you use this guide you will become familiar with the following types of ratios: • Common size ratios • Liquidity ratios • Efficiency ratios • Solvency ratios One of the most useful ways for the owner of a small business to look at the company's financial statements is by using "common size" ratios. Common size ratios can be developed from both balance sheet and income statement items. The phrase "common size ratio" may be unfamiliar to you, but it is simple in concept and just as simple to create. You just calculate each line item on the statement as a percentage of the total. For example, each of the items on the income statement would be calculated as a percentage of total sales. (Divide each line item by total sales, then multiply each one by 100 to turn it into a percentage.) Similarly, items on the balance sheet would be calculated as percentages of total assets (or total liabilities plus owner's equity.) This simple process converts numbers on your financial statements into information that you can use to make period-to-period and company-to-company comparisons. If you want to evaluate your cash position compared to the cash position of one of your key competitors, you need more information than what you have, say,$12,000 and he or she has $22,000. That's a lot less informative than knowing that your company's cash is equal to 7% of total assets, while your competitor's cash is 9% of their assets. Common size ratios make comparisons more meaningful they provide a context for your data. Common Size Ratios from the Balance Sheet To calculate common size ratios from your balance sheet, simply compute every asset category as a percentage of total assets, and every liability account as a percentage of total liabilities plus owners' equity. Here is what a common size balance sheet looks like for the mythical Doobie Company: ABC Company Common Size Balance Sheet For the year ending December 31, 200x Assets$ % Current Assets Cash 12,000 6.6% Marketable Securities 10,000 5.5% Accounts Receivable (net of uncollectible accounts) 17,000 9.4% Inventory 22,000 12.2% Prepaid Expense 4,000 2.2% Total Current Assets 65,000 35.9% Fixed Assets Building and Equipment 105,000 58.3% Less Depreciation 30,000 16.6% Net Buildings and Equipment 75,000 41.6% Land 40,000 22.2% Total Fixed Assets 115,000 63.8% Total Assets 180,000 100.0% Liabilities Current Liabilities Wages Payable 3,000 1.6% Accounts Payable 25,000 13.8% Taxes Payable 12,000 6.6% Total Current Liabilities 40,000 22.2% Long-Term Liabilities Mortgage Payable 70,000 38.8% Note Payable 15,000 8.3% Deferred Taxes 15,000 8.3% Total Long-Term Liabilities 100,000 55.5% Total Liabilities 140,000 77.7% Owner's Equity 40,000 22.2% Total Liabilities and Owner's Equity 180,000 100.0%

In the example for Doobie Company, cash is shown as being 6.6% of total assets. This percentage is the result of the following calculation:

(Multiplying by 100 converts the ratio into a percentage.)

Common size ratios translate data from the balance sheet, such as the fact that there is $12,000 in cash, into the information that 6.6% of Doobie Company's total assets are in cash. Additional information can be developed by adding relevant percentages together, such as the realization that 11.7% (6.6% + 5.1%) of Doobie's total assets are in cash and marketable securities. Common size ratios are a simple but powerful way to learn more about your business. This type of information should be computed and analyzed regularly. As a small business owner, you should pay particular attention to trends in accounts receivables and current liabilities. Receivables should not be tying up an undue amount of company assets. If you see accounts receivables increasing dramatically over several periods, and it is not a planned increase, you need to take action. This might mean stepping up your collection practices, or putting tighter limits on the credit you extend to your customers. As this example illustrates, the point of doing financial ratio analysis is not to collect statistics about your company, but to use those numbers to spot the trends that are affecting your company. Ask yourself why key ratios are up or down compared to prior periods or to your competitors. The answers to those questions can make an important contribution to your decision-making about the future of your company. Current ratio analysis is also a very helpful way for you to evaluate how your company uses its cash. Obviously it is vital to have enough cash to pay current liabilities, as your landlord and the electric company will tell you. The balance sheet for the Doobie Company shows that the company can meet current liabilities. The line items of "total current liabilities,"$40,000, is substantially lower than "total current assets," $65,000. But you may wonder, "How do I know if my current ratio is out of line for my type of business?" You can answer this question (and similar questions about any other ratio) by comparing your company with others. You may be able to convince competitors to share information with you, or perhaps a trade association for your industry publishes statistical information you can use. If not, you can use any of the various published compilations of financial ratios. (See the Resources section at the end of this document.) Because financial ratio comparisons are so important for bank loan officers who make loans to businesses, RMA (formerly a bankers' trade association, Robert Morris Associates) has for many years published a volume called "Annual Statement Studies." These contain ratios for more than 300 industries, broken down by asset size and sales size. RMA's "Annual Statement Studies" are available in most public and academic libraries, or you may ask your banker to obtain the information you need. Another source of information is "Industry Norms and Key Business Ratios," published by Dun and Bradstreet. It is compiled from D&B's vast databases of information on businesses. It lists financial ratios for hundreds of industries, and is available in academic and public libraries that serve business communities. These and similar publications will give you an industry standard or "benchmark" you can use to compare your firm to others. The ratios described in this guide, and many others, are included in these publications. While period-to-period comparisons based on your own company's data are helpful, comparing your company's performance with other similar businesses can be even more informative. Compute common size ratios using your company's balance sheet. Common Size Ratios from the Income Statement To prepare common size ratios from your income statement, simply calculate each income account as a percentage of sales. This converts the income statement into a powerful analytical tool. Here is what a common size income statement looks like for the fictional Doobie Company:$ % Sales $200,000 100% Cost of goods sold 130,000 65% Gross Profit 70,000 35% Operating expenses Selling expenses 22,000 11% General e xpenses 10,000 5% Administrative expenses 4,000 2% Total operating expenses 36,000 18% Operating income 34,000 17% Other income 2,500 1% Interest expense 500 0% Income before taxes 36,000 18% Income taxes 1,800 1% Net profit 34,200 17% Common size ratios allow you to make knowledgeable comparisons with past financial statements for your own company and to assess trends&mdashboth positive and negative&mdashin your financial statements. The gross profit margin and the net profit margin ratios are two common size ratios to which small business owners should pay particular attention. On a common size income statement, these margins appear as the line items "gross profit" and "net profit." For the Doobie Company, the common size ratios show that the gross profit margin is 35% of sales. This is computed by dividing gross profit by sales (and multiplying by 100 to create a percentage.)$70,000/200,000 x 100 = 35%

Even small changes of 1% or 2% in the gross profit margin can affect a business severely. After all, if your profit margin drops from 5% of sales to 4%, that means your profits have declined by 20%.

Remember, your goal is to use the information provided by the common size ratios to start asking why changes have occurred, and what you should do in response. For example, if profit margins have declined unexpectedly, you probably will want to closely examine all expenses&mdashagain, using the common size ratios for expense line items to help you spot significant changes.

Compute common size ratios from your income statement.

Look at the gross profit and net profit margins as a percentage of sales. Compare these percentages with the same items from your income statement of a year ago. Are any fluctuations favorable or not? Do you know why they changed?

Liquidity ratios measure your company's ability to cover its expenses. The two most common liquidity ratios are the current ratio and the quick ratio. Both are based on balance sheet items.

The current ratio is a reflection of financial strength. It is the number of times a company's current assets exceed its current liabilities, which is an indication of the solvency of that business.

Here is the formula to compute the current ratio.

Current Ratio = Total current assets/Total current liabilities

Using the earlier balance sheet data for the mythical Doobie Company, we can compute the company's current ratio.

Doobie Company Current Ratio:

This tells the owners of the Doobie Company that current liabilities are covered by current assets 1.6 times. The current ratio answers the question, "Does the business have enough current assets to meet the payment schedule of current liabilities, with a margin of safety?"

A common rule of thumb is that a "good" current ratio is 2 to 1. Of course, the adequacy of a current ratio will depend on the nature of the business and the character of the current assets and current liabilities. There is usually very little uncertainty about the amount of debts that are due, but there can be considerable doubt about the quality of accounts receivable or the cash value of inventory. That's why a safety margin is needed.

A current ratio can be improved by increasing current assets or by decreasing current liabilities. Steps to accomplish an improvement include:

• Paying down debt.
• Acquiring a long-term loan (payable in more than 1 year's time).
• Selling a fixed asset.
• Putting profits back into the business.

A high current ratio may mean that cash is not being utilized in an optimal way. For example, the excess cash might be better invested in equipment.

The Quick Ratio is also called the "acid test" ratio. That's because the quick ratio looks only at a company's most liquid assets and compares them to current liabilities. The quick ratio tests whether a business can meet its obligations even if adverse conditions occur.

Here is the formula for the quick ratio:

Quick Ratio = (Current Assets − Inventory)/Current Liabilities

Assets considered to be "quick" assets include cash, stocks and bonds, and accounts receivable (in other words, all of the current assets on the balance sheet except inventory.)

Using the balance sheet data for the Doobie Company, we can compute the quick ratio for the company.

Quick ratio for the Doobie Company:

(65,000 − 22,000)/40,000 = 1.07

In general, quick ratios between 0.5 and 1 are considered satisfactory&mdashas long as the collection of receivables is not expected to slow. So the Doobie Company seems to have an adequate quick ratio.

Compute a current ratio and a quick ratio using your company's balance sheet data.

There are many types of ratios that you can use to measure the efficiency of your company's operations. In this section we will look at four that are widely used. There may be others that are common to your industry, or that you will want to create for a specific purpose within your company.

The four ratios we will look at are:

• Inventory Turnover Ratio
• Sales to Receivables Ratio
• Days' Receivables Ratio
• Return on Assets

The inventory turnover ratio measures the number of times inventory "turned over" or was converted into sales during a time period. It is also known as the cost-of-sales to inventory ratio. It is a good indication of purchasing and production efficiency.

The data used to calculate this ratio come from both the company's income statement and balance sheet. Here is the formula:

Inventory Ratio = Cost of Goods Sold/Inventory

Using the financial statements for the Doobie Company, we can compute the following inventory turnover ratio for the company:

In general, the higher a cost of sales to inventory ratio, the better. A high ratio shows that inventory is turning over quickly and that little unused inventory is being stored.

Sales-to-Receivables Ratio

The sales-to-receivables ratio measures the number of times accounts receivables turned over during the period. The higher the turnover of receivables, the shorter the time between making sales and collecting cash. The ratio is based on NET sales and NET receivables. (A reminder: net sales equals sales less any allowances for returns or discounts. Net receivables equals accounts receivable less any adjustments for bad debts.)

This ratio also uses information from both the balance sheet and the income statement. It is calculated as follows:

Sales-to-Receivables Ratio = Net Sales/Net Receivables

Using the financial statements for the Doobie Company (and assuming that the Sales reported on their income statement is net Sales), we can compute the following sales- to-receivables ratio for the company:

Doobie Company Sales-to-Receivables Ratio:

This means that receivables turned over nearly 12 times during the year. This is a ratio that you will definitely want to compare to industry standards. Keep in mind that its significance depends on the amount of cash sales a company has. For a company without many cash sales, it may not be important. Also, it is a measure at only one point in time and does not take into account seasonal fluctuations.

Days' Receivables Ratio

The days' receivables ratio measures how long accounts receivable are outstanding. Business owners will want as low a days' receivables ratio as possible. After all, you want to use your cash to build your company, not to finance your customers. Also, the likelihood of nonpayment typically increases as time passes.

It is computed using the sales/receivables ratio. Here is the formula:

Days' Receivables Ratio = 365/Sales Receivables Ratio

The "365" in the formula is simply the number of days in the year. The sales receivable ratio is taken from the calculation we did just a few paragraphs earlier.

Using the financial statements for the Doobie Company, we can compute the following day's receivables ratio for the company.

Doobie Company Days' Receivables Ratio

This means that receivables are outstanding an average of 31 days. Again, the real meaning of the number will only be clear if you compare your ratios to others in the industry.

The return on assets ratio measures the relationship between profits your company generated and assets that were used to generate those profits. Return on assets is one of the most common ratios for business comparisons. It tells business owners whether they are earning a worthwhile return from the wealth tied up in their companies. In addition, a low ratio in comparison to other companies may indicate that your competitors have found ways to operate more efficiently. Publicly held companies commonly report return on assets to shareholders it tells them how well the company is using its assets to produce income.

It is computed as follows:

Return on Assets = Net Income Before Taxes/Total Assets X 100

(Multiplying by 100 turns the ratio into a percentage.)

Using the balance sheet and income statement for the Doobie Company, we can compute the return on assets ratio for the company:

Doobie Company Return on Assets:

$36,000/180,000 x 100 = 20% This is a ratio that you will certainly want to compare with other firms in your industry. Solvency ratios measure the stability of a company and its ability to repay debt. These ratios are of particular interest to bank loan officers. They should be of interest to you, too, since solvency ratios give a strong indication of the financial health and viability of your business. We will look at the following solvency ratios: • Debt-to-worth ratio • Working capital • Net sales to working capital • Z-Score The debt-to-worth ratio (or leverage ratio) is a measure of how dependent a company is on debt financing as compared to owner's equity. It shows how much of a business is owned and how much is owed. The debt-to-worth ratio is computed as follows: Debt-to-Worth Ratio = Total Liabilities/Net Worth (A reminder: Net Worth = Total Assets Minus Total Liabilities.) Using balance sheet data for the Doobie Company, we can compute the debt-to-worth ratio for the company. Doobie Company debt-to-worth ratio: If the debt-to-worth ratio is greater than 1, the capital provided by lenders exceeds the capital provided by owners. Bank loan officers will generally consider a company with a high debt-to-worth ratio to be a greater risk. Debt-to-worth ratios will vary with the type of business and the risk attitude of management. Working capital is a measure of cash flow, and not a real ratio. It represents the amount of capital invested in resources that are subject to relatively rapid turnover (such as cash, accounts receivable and inventories) less the amount provided by short-term creditors. Working capital should always be a positive number. Lenders use it to evaluate a company's ability to weather hard times. Loan agreements often specify that the borrower must maintain a specified level of working capital. Working capital is computed as follows: Working Capital = Total Current Assets − Total Current Liabilities Using the balance sheet data for the Doobie Company, we can compute the working capital amount for the company. Doobie Company working capital: Doobie Company has$25,000 in working capital

Net Sales to Working Capital

The relationship between net sales and working capital is a measurement of the efficiency in the way working capital is being used by the business. It shows how working capital is supporting sales.

It is computed as follows:

Net Sales to Working Capital Ratio = Net Sales/Net Working Capital

Using balance sheet data for the Doobie Company and the working capital amount computed in the previous calculation, we compute the net sales to working capital as follows:

Doobie Company Net Sales to Working Capital Ratio

Again, this is a ratio that must be compared to others in your industry to be meaningful. In general, a low ratio may indicate an inefficient use of working capital that is, you could be doing more with your resources, such as investing in equipment. A high ratio can be dangerous, since a drop in sales which causes a serious cash shortage could leave your company vulnerable to creditors.

The Z-Score is at the end of our list neither because it is the least important, nor because it's at the end of the alphabet. It's here because it's a bit more complicated to calculate. In return for doing a little more arithmetic, however, you get a number&mdasha Z-Score&mdashwhich most experts regard as a very accurate guide to your company's financial solvency. In blunt terms, a Z-Score of 1.81 or below means you are headed for bankruptcy. One of 2.99 means your company is sound.

The Z-Score was developed by Edward I. Altman, a professor at the Leonard N. Stern School of Business at New York University. Dr. Altman researched dozens of companies that had gone bankrupt, and others that were doing well. He eventually focused on five key balance sheet ratios. He assigned a weight to each of the five, multiplying each ratio by a number he derived from his research to indicate its relative importance. The sum of the weighted ratios is the Z-Score.

Calculating The Z-Score

Earnings Before
Interest and Taxes /
Total Assets

Market Value of Equity / Total Liabilities

Working Capital
to Total Assets

Working Capital /
Total Assets

Retained Earnings
to Total Assets

Retained Earnings /
Total Assets

x 1.4 Total of all Weighted Ratios = Z-Score:

Like many other ratios, the Z-Score can be used both to see how your company is doing on its own, and how it compares to others in your industry.

For a worksheet on calculating your Z-Score. Click below:

Calculate the debt to worth ratio, working capital, and net sales to working capital ratio for your company. How do your ratios compare to others in your industry?

This document has presented information on common size ratios for both the income statement and the balance sheet, plus several additional financial ratios you can use to gain a better understanding of the financial health of your business.

The ratios you will use most frequently are common size ratios from the income statement, the current ratio, the quick ratio and return on assets. Your specific type of business may require you to use some or all of the other ratios as well.

Financial ratio analysis is one way to turn financial statements, with their long columns of numbers, into powerful business tools. Financial ratio analysis offers a simple solution to numbers overload.

___ When computing common size ratios for your company's balance sheet, were percentages for asset categories based on total assets? Were liability percentages based on total liabilities plus owners' equity?

___ Have you examined at least one source of comparative financial ratios?

___ Is your quick ratio between 0.5 and 1? If not, is there an explanation that is satisfactory to you?

___ When computing the sales-to-receivables ratio, did you remember to use NET sales and NET receivables?

___ Does the net sales-to-working capital ratio that you computed make sense for your business? Are adjustments necessary?

___ Where is your company's Z-Score? If it is low, or the trend is down for recent years, do you know what changes you need to make?

Sources of Information on Profitability Analysis

Budgeting and Finance (First Books for Business) by Peter Engel. (McGraw-Hill, 1996).

Fundamentals of Financial Management, 11th ed. by James C. Van Horne and John Martin Wachowicz. (Prentice Hall, 2001).

Sources of Information on Financial Ratios

RMA Annual Statement Studies, Risk Management Association. Data for 325 lines of business, sorted by asset size and by sales volume to allow comparisons to companies of similar size in the same industry. The "common size" (percentage of total assets or sales) is provided for each balance sheet and income statement item.

Almanac of Business and Industrial Financial Ratios, annual, by Leo Troy. (Prentice-Hall, Inc.). Information for 150 industries on 22 financial categories. Data is usually three years prior to the publication date.

Financial Studies of the Small Business by Karen Goodman. Financial Research Associates. Focusing on business with capitalizations under \$1 million, providing financial ratios and other information.

Industriscope: Comprehensive Data for Industry Analysis. Media General Financial Services. Compare company-to-company, company-to-industry & industry-to-industry 215 industry groups over 9,000 companies grouped within their industry over 40 key items listed on each company & industry price, price change & relative price data shareholdings data revenue, earnings & dividend data ratio analysis historical archives available back to May 1973.

Kauffman Business EKG, Kauffman Center for Entrepreneurial Leadership. A fill-in-the-blanks calculator for several income and sales ratios.

Writer: Alex Auerbach

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